circuit analysis - How to efficiently compute the current at each node in a resistor network

I encountered a academic research problem to efficiently compute the current/voltage at each node of a rectangular resistor network. The rectangular resistor network that I have is defined by two things 1) the regular network topology, which you can consider it like meshgrids with one unit resistor on each edge; and 2) the knowledge of the state of each node (bad or good). For example, a 2x2 resistor network of my type (with all good node) is

^{simulate this circuit – Schematic created using CircuitLab}

3x3 resistor networks of my type with all good nodes and one bad node(2,0) are given below.

^{simulate this circuit}

In practice, a resistor network I might have to deal with is of size 300x500. I wonder whether there is some efficient method to compute the current/voltage at each node, when the good/bad nodes are known and the two nodes connected into the circuit is (0,0) and (299,499). I guess there should be some existing methods to this type of questions. Can anyone kindly help me?